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Mathematics

2 answers:

GaryK [48]3 years ago

8 0

Answer is:

s = 50

Here's how to solve:

In this inequality, our first step is to find the least common denominator (that applies to both fractions, of course), or LCD. For the LCD, the we must find a number that is a multiple of both 21 and 30, and then multiply both sides of the inequality by said value. The reason we multiply on both sides of the inequality is because of the Line of Equality, which is a ruling that states that what you do on one side of an inequality, you also must do on the other.

In this case, our LCD is 210. After multiplying both sides, we are left with 350 = 7s.

Our next step is to isolate the variable 7s to make it singular. 1s, or s, is what we are trying to change the variable to, since that is what the isolated variable will look like. By dividing 7s by 7, we can successfully isolate the variable to 1s/s. Due to the Line of Equality rule, we should do this to both sides. After dividing each side by 7, we are left with s = 50.

Therefore, the value of s is 50, making the answer s = 50.

<h3>Bonus: Showing Work</h3>

Finding the LCD;

LCD for 21:

( 21 * 1 , 21 * 2 , 21 * 3 , 21 * 4 , etc... )

Multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, 231, 252, 273

LCD for 30:

( 30 * 1 , 30 * 2 , 30 * 3 , 30 * 4 , etc... )

Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300

LCD Found; 210

Multiplying by LCD;

( 35 / 21 * 210 or 35 ÷ 21 * 210 )

Left Side Steps:

Simplify- 35 / 21 --> 35 ÷ 7 / 21 ÷ 7 --> 35 ÷ 7 = 5 & 21 ÷ 7 = 3 --> 5 / 3 ( * 210 )

Single Fraction Format/Format Change- 5 / 3 * 210 --> 5 * 210 / 3

Multiply Numerator(s)/Top- 5 * 210 / 3 --> 5 * 210 = 1050 --> 1050 / 3

Divide Numerator & Denominator- 1050 / 3 or 1050 ÷ 3 --> 350

Right Side Steps:

( s / 30 * 210 or s ÷ 30 * 210 )

Single Fraction Format/Format Change- s / 30 * 210 --> s * 210 / 30

Multiply Numerator(s)/Top- s * 210 / 30 --> 210s / 30

Divide Numerator & Denominator- 210s / 30 or 210s ÷ 30 --> 7s

New Inequality/Equation Found: 350 = 7s

Dividing by 7;

Left Side: 350 ÷ 7 = 50

Right Side: 7s ÷ 7 = s

New Inequality Found; 50 = s, or s = 50 (the sign does not flip because the equivalent sign is the same both ways - and the opposite would be the same as the current value)

Hope this helps! :]